STATISTICS

UK Tourism: Data Analysis



PART ONE

Derive a scatter graph to show the relationship between the number of overseas visitors and the earnings from these visits

Scattered Diagram

Explaination

The above diagram shows that earnig from visits made by foriegners has direct relation with the number of visits they make to UK. That means, as the ovearseas visits increases the earning will increase na das the visits decrease the earning will also decrease.

Derive a scatter graph to shown the relationship between the number of UK residents going abroad and the expenditure made during these visits.

Scattered Diagram

Explaination

The above scattered diagram shows that expenditures from visits made by UK residents has direct relation with the number of visits they make to abroad. That means, as the residents' visits to abroad increase the expenditureswill increase and as the visits decrease the expenditure will also decrease.

Determine the correlation coefficients and coefficients of determination linking the number of visits and earnings /expenditures for both UK residents going abroad and overseas visitors to the UK.

Coefficient of correlation (r) and coefficient of determination (R2)

To calculate (r) and R2, first we have to calculate standard mean and deviation standard deviation of the given data.

We will calculate the standard deviation with the help of spread sheet (Ms excel)

Mean ((overseas visits to UK) = 7446

Standard deviation (overseas visits to UK) = 1278.928566

Standard deviation (overseas visits to UK earning) = 887.7187611

Mean (overseas visits to UK earning) = 3710.233333

Coefficient of correlation = rjk = ((xij - j)(xik - k)) / njk

We calculate r with the help of spread sheet.

r = 0.93842621

r shows the tendency of relationship between dependent and independent variables, higher the value of r stronger the relationship between variables. Moreover, negative value shows the inverse relationship between dependent and independent variable. Here, the value of r (0.94 approx) shows the strong correlation between earning and the visits made by foreigners. Value of r says, if 0.94 visits are made by foreigner will generate income of 1 pound for UK and vice versa.

R2 = (93842621)2 = 0.880643751

R2, the coefficient of determination shows the tendency of variation made by independent variable in dependent variable, higher the value higher the contribution of independent variable in the variation of dependent variable. Value of R2 (0.88) show that visits made by foreigner are causing 88% variation in earning made by UK.

UK residents' visits to abroad correlation with UK residents' visits to abroad expenditure

Mean (UK residents' visits to abroad) = 16106.36667

Standard deviation (UK residents' visits to abroad) = 3761.931964

Standard deviation (UK residents' visits to abroad expenditures) = 2029.269945

Mean (UK residents' visits to abroad expenditures) = 8100.2

Coefficient of correlation = rjk = ((xij - j)(xik - k)) / njk

We calculate r with the help of spread sheet.

r = 0.953351675

Here, the value of r (0.95 approx) shows the strong correlation between expenditure and the visits made by foreigners. Value of r says, if 0.95 visits are made by UK residents will increase expenditures by 1 pound for UK and vice versa.

R2 = (93842621)2 = ...